vladislavbelov
ffc4a56b9f
Fixes #6846 Differential Revision: https://code.wildfiregames.com/D5185 This was SVN commit r27965.
317 lines
7.2 KiB
C++
317 lines
7.2 KiB
C++
/* Copyright (C) 2009 Wildfire Games.
|
|
* This file is part of 0 A.D.
|
|
*
|
|
* 0 A.D. is free software: you can redistribute it and/or modify
|
|
* it under the terms of the GNU General Public License as published by
|
|
* the Free Software Foundation, either version 2 of the License, or
|
|
* (at your option) any later version.
|
|
*
|
|
* 0 A.D. is distributed in the hope that it will be useful,
|
|
* but WITHOUT ANY WARRANTY; without even the implied warranty of
|
|
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
|
* GNU General Public License for more details.
|
|
*
|
|
* You should have received a copy of the GNU General Public License
|
|
* along with 0 A.D. If not, see <http://www.gnu.org/licenses/>.
|
|
*/
|
|
|
|
#include "precompiled.h"
|
|
|
|
#include "Quaternion.h"
|
|
|
|
#include "MathUtil.h"
|
|
#include "Matrix3D.h"
|
|
|
|
const float EPSILON=0.0001f;
|
|
|
|
|
|
CQuaternion::CQuaternion() :
|
|
m_W(1)
|
|
{
|
|
}
|
|
|
|
CQuaternion::CQuaternion(float x, float y, float z, float w) :
|
|
m_V(x, y, z), m_W(w)
|
|
{
|
|
}
|
|
|
|
CQuaternion CQuaternion::operator + (const CQuaternion &quat) const
|
|
{
|
|
CQuaternion Temp;
|
|
Temp.m_W = m_W + quat.m_W;
|
|
Temp.m_V = m_V + quat.m_V;
|
|
return Temp;
|
|
}
|
|
|
|
CQuaternion &CQuaternion::operator += (const CQuaternion &quat)
|
|
{
|
|
*this = *this + quat;
|
|
return *this;
|
|
}
|
|
|
|
CQuaternion CQuaternion::operator - (const CQuaternion &quat) const
|
|
{
|
|
CQuaternion Temp;
|
|
Temp.m_W = m_W - quat.m_W;
|
|
Temp.m_V = m_V - quat.m_V;
|
|
return Temp;
|
|
}
|
|
|
|
CQuaternion &CQuaternion::operator -= (const CQuaternion &quat)
|
|
{
|
|
*this = *this - quat;
|
|
return *this;
|
|
}
|
|
|
|
CQuaternion CQuaternion::operator * (const CQuaternion &quat) const
|
|
{
|
|
CQuaternion Temp;
|
|
Temp.m_W = (m_W * quat.m_W) - (m_V.Dot(quat.m_V));
|
|
Temp.m_V = (m_V.Cross(quat.m_V)) + (quat.m_V * m_W) + (m_V * quat.m_W);
|
|
return Temp;
|
|
}
|
|
|
|
CQuaternion &CQuaternion::operator *= (const CQuaternion &quat)
|
|
{
|
|
*this = *this * quat;
|
|
return *this;
|
|
}
|
|
|
|
CQuaternion CQuaternion::operator * (float factor) const
|
|
{
|
|
CQuaternion Temp;
|
|
Temp.m_W = m_W * factor;
|
|
Temp.m_V = m_V * factor;
|
|
return Temp;
|
|
}
|
|
|
|
|
|
float CQuaternion::Dot(const CQuaternion& quat) const
|
|
{
|
|
return
|
|
m_V.X * quat.m_V.X +
|
|
m_V.Y * quat.m_V.Y +
|
|
m_V.Z * quat.m_V.Z +
|
|
m_W * quat.m_W;
|
|
}
|
|
|
|
void CQuaternion::FromEulerAngles (float x, float y, float z)
|
|
{
|
|
float cr, cp, cy;
|
|
float sr, sp, sy;
|
|
|
|
CQuaternion QRoll, QPitch, QYaw;
|
|
|
|
cr = cosf(x * 0.5f);
|
|
cp = cosf(y * 0.5f);
|
|
cy = cosf(z * 0.5f);
|
|
|
|
sr = sinf(x * 0.5f);
|
|
sp = sinf(y * 0.5f);
|
|
sy = sinf(z * 0.5f);
|
|
|
|
QRoll.m_V = CVector3D(sr, 0, 0);
|
|
QRoll.m_W = cr;
|
|
|
|
QPitch.m_V = CVector3D(0, sp, 0);
|
|
QPitch.m_W = cp;
|
|
|
|
QYaw.m_V = CVector3D(0, 0, sy);
|
|
QYaw.m_W = cy;
|
|
|
|
(*this) = QYaw * QPitch * QRoll;
|
|
}
|
|
CVector3D CQuaternion::ToEulerAngles()
|
|
{
|
|
float heading, attitude, bank;
|
|
float sqw = m_W * m_W;
|
|
float sqx = m_V.X*m_V.X;
|
|
float sqy = m_V.Y*m_V.Y;
|
|
float sqz = m_V.Z*m_V.Z;
|
|
float unit = sqx + sqy + sqz + sqw; // if normalised is one, otherwise is correction factor
|
|
float test = m_V.X*m_V.Y + m_V.Z*m_W;
|
|
if (test > (.5f-EPSILON)*unit)
|
|
{ // singularity at north pole
|
|
heading = 2 * atan2( m_V.X, m_W);
|
|
attitude = (float)M_PI/2;
|
|
bank = 0;
|
|
}
|
|
else if (test < (-.5f+EPSILON)*unit)
|
|
{ // singularity at south pole
|
|
heading = -2 * atan2(m_V.X, m_W);
|
|
attitude = -(float)M_PI/2;
|
|
bank = 0;
|
|
}
|
|
else
|
|
{
|
|
heading = atan2(2.f * (m_V.X*m_V.Y + m_V.Z*m_W),(sqx - sqy - sqz + sqw));
|
|
bank = atan2(2.f * (m_V.Y*m_V.Z + m_V.X*m_W),(-sqx - sqy + sqz + sqw));
|
|
attitude = asin(-2.f * (m_V.X*m_V.Z - m_V.Y*m_W));
|
|
}
|
|
return CVector3D(bank, attitude, heading);
|
|
}
|
|
|
|
CMatrix3D CQuaternion::ToMatrix () const
|
|
{
|
|
CMatrix3D result;
|
|
ToMatrix(result);
|
|
return result;
|
|
}
|
|
|
|
void CQuaternion::ToMatrix(CMatrix3D& result) const
|
|
{
|
|
float wx, wy, wz, xx, xy, xz, yy, yz, zz;
|
|
|
|
// calculate coefficients
|
|
xx = m_V.X * m_V.X * 2.f;
|
|
xy = m_V.X * m_V.Y * 2.f;
|
|
xz = m_V.X * m_V.Z * 2.f;
|
|
|
|
yy = m_V.Y * m_V.Y * 2.f;
|
|
yz = m_V.Y * m_V.Z * 2.f;
|
|
|
|
zz = m_V.Z * m_V.Z * 2.f;
|
|
|
|
wx = m_W * m_V.X * 2.f;
|
|
wy = m_W * m_V.Y * 2.f;
|
|
wz = m_W * m_V.Z * 2.f;
|
|
|
|
result._11 = 1.0f - (yy + zz);
|
|
result._12 = xy - wz;
|
|
result._13 = xz + wy;
|
|
result._14 = 0;
|
|
|
|
result._21 = xy + wz;
|
|
result._22 = 1.0f - (xx + zz);
|
|
result._23 = yz - wx;
|
|
result._24 = 0;
|
|
|
|
result._31 = xz - wy;
|
|
result._32 = yz + wx;
|
|
result._33 = 1.0f - (xx + yy);
|
|
result._34 = 0;
|
|
|
|
result._41 = 0;
|
|
result._42 = 0;
|
|
result._43 = 0;
|
|
result._44 = 1;
|
|
}
|
|
|
|
void CQuaternion::Slerp(const CQuaternion& from, const CQuaternion& to, float ratio)
|
|
{
|
|
float to1[4];
|
|
float omega, cosom, sinom, scale0, scale1;
|
|
|
|
// calc cosine
|
|
cosom = from.Dot(to);
|
|
|
|
|
|
// adjust signs (if necessary)
|
|
if (cosom < 0.0)
|
|
{
|
|
cosom = -cosom;
|
|
to1[0] = -to.m_V.X;
|
|
to1[1] = -to.m_V.Y;
|
|
to1[2] = -to.m_V.Z;
|
|
to1[3] = -to.m_W;
|
|
}
|
|
else
|
|
{
|
|
to1[0] = to.m_V.X;
|
|
to1[1] = to.m_V.Y;
|
|
to1[2] = to.m_V.Z;
|
|
to1[3] = to.m_W;
|
|
}
|
|
|
|
// calculate coefficients
|
|
if ((1.0f - cosom) > EPSILON)
|
|
{
|
|
// standard case (slerp)
|
|
omega = acosf(cosom);
|
|
sinom = sinf(omega);
|
|
scale0 = sinf((1.0f - ratio) * omega) / sinom;
|
|
scale1 = sinf(ratio * omega) / sinom;
|
|
}
|
|
else
|
|
{
|
|
// "from" and "to" quaternions are very close
|
|
// ... so we can do a linear interpolation
|
|
scale0 = 1.0f - ratio;
|
|
scale1 = ratio;
|
|
}
|
|
|
|
// calculate final values
|
|
m_V.X = scale0 * from.m_V.X + scale1 * to1[0];
|
|
m_V.Y = scale0 * from.m_V.Y + scale1 * to1[1];
|
|
m_V.Z = scale0 * from.m_V.Z + scale1 * to1[2];
|
|
m_W = scale0 * from.m_W + scale1 * to1[3];
|
|
}
|
|
|
|
void CQuaternion::Nlerp(const CQuaternion& from, const CQuaternion& to, float ratio)
|
|
{
|
|
float c = from.Dot(to);
|
|
if (c < 0.f)
|
|
*this = from - (to + from) * ratio;
|
|
else
|
|
*this = from + (to - from) * ratio;
|
|
Normalize();
|
|
}
|
|
|
|
///////////////////////////////////////////////////////////////////////////////////////////////
|
|
// FromAxisAngle: create a quaternion from axis/angle representation of a rotation
|
|
void CQuaternion::FromAxisAngle(const CVector3D& axis, float angle)
|
|
{
|
|
float sinHalfTheta=(float) sin(angle/2);
|
|
float cosHalfTheta=(float) cos(angle/2);
|
|
|
|
m_V.X=axis.X*sinHalfTheta;
|
|
m_V.Y=axis.Y*sinHalfTheta;
|
|
m_V.Z=axis.Z*sinHalfTheta;
|
|
m_W=cosHalfTheta;
|
|
}
|
|
|
|
///////////////////////////////////////////////////////////////////////////////////////////////
|
|
// ToAxisAngle: convert the quaternion to axis/angle representation of a rotation
|
|
void CQuaternion::ToAxisAngle(CVector3D& axis, float& angle)
|
|
{
|
|
CQuaternion q = *this;
|
|
q.Normalize();
|
|
angle = acosf(q.m_W) * 2.f;
|
|
float sin_a = sqrtf(1.f - q.m_W * q.m_W);
|
|
if (fabsf(sin_a) < 0.0005f) sin_a = 1.f;
|
|
axis.X = q.m_V.X / sin_a;
|
|
axis.Y = q.m_V.Y / sin_a;
|
|
axis.Z = q.m_V.Z / sin_a;
|
|
}
|
|
|
|
|
|
///////////////////////////////////////////////////////////////////////////////////////////////
|
|
// Normalize: normalize this quaternion
|
|
void CQuaternion::Normalize()
|
|
{
|
|
float lensqrd=SQR(m_V.X)+SQR(m_V.Y)+SQR(m_V.Z)+SQR(m_W);
|
|
if (lensqrd>0) {
|
|
float invlen=1.0f/sqrtf(lensqrd);
|
|
m_V*=invlen;
|
|
m_W*=invlen;
|
|
}
|
|
}
|
|
|
|
///////////////////////////////////////////////////////////////////////////////////////////////
|
|
|
|
CVector3D CQuaternion::Rotate(const CVector3D& vec) const
|
|
{
|
|
// v' = q * v * q^-1
|
|
// (where v is the quat. with w=0, xyz=vec)
|
|
|
|
return (*this * CQuaternion(vec.X, vec.Y, vec.Z, 0.f) * GetInverse()).m_V;
|
|
}
|
|
|
|
CQuaternion CQuaternion::GetInverse() const
|
|
{
|
|
// (x,y,z,w)^-1 = (-x/l^2, -y/l^2, -z/l^2, w/l^2) where l^2=x^2+y^2+z^2+w^2
|
|
// Since we're only using quaternions for rotation, they should always have unit
|
|
// length, so assume l=1
|
|
return CQuaternion(-m_V.X, -m_V.Y, -m_V.Z, m_W);
|
|
}
|